The unprecedented combination of spatial resolution and stability achieved by the Solar Oscillations Investigation/Michelson Doppler Imager on SOHO has opened up new opportunities for the analysis of solar surface oscillations of high spatial frequencies. In this regime the oscillations are essentially plane waves, amenable to the techniques of ring-diagram analysis of their three-dimensional power spectra. This approach holds the promise of measuring fluid motions and possibly magnetic fields in spatially-resolved structures within the uppermost levels of the convective envelope, a region unresolved by the global modes. Atmospheric g-modes trapped above the photosphere may also be detectable. We review the first results of plane-wave analysis of various types of SOI data and comparisons with the analyses of comparable ground-based datasets.